Summary

This report addresses the assessment of the extent to which the racial composition of North Carolina boards of county commissioners represent that of their respective counties. I have used a simulation of random selections from the 2016 ACS county populations in this assessment. This study uses four race categories, American Indian, Black, White, and Other. The simulation results in identifying over one-half the counties where the actual 2016 board of county commissioners racial composition, as reported by the NCACC, was representative of the county population. To a significant extent this follows from there being thirty four counties that have fewer than ten percent Black residents, where accordingly there are few likely outcomes. I also utilize a diversity index to make semi-quantitative statements about the counties. The simulation and the diversity methods are independent of each other, providing two ways to assess representation. This analysis suggests that there are seventeen counties where the computed lack of representation merits further study.

Methodology

The purpose of this report is to assess the representativeness of the racial composition of boards of county commissioners with respect to that of their constituents. I will first utilize a methodology that treats this as a combinatorial problem, where the results of sampling constituents is compared to board compositions. The sampling is carried out by use of simulations based on either Census Bureau American Community Survey estimates, or NCSBE voter turnout records, and is compared with NCACC board compositions.

An inherent property of simulations is the variability of results. This variability is a consequence of the use of different randomization seeds, and also from using different numbers of simulation runs. This is compounded by the population estimates, which are indeed, just estimates. Even in the decadal censuses, populations are estimates. Another contributing factor is that race reporting is shaped by being self-reported and using categories that are somewhat different for the Census Bureau, NCSBE,and possibly for the NCACC.

As a consequence of this, results from simulations must not be over-interpreted. Small differences in the assessments between counties or over years, are of minor consequence. “Small”, however, needs to be determined as the analysis progresses. Practically, this mitigates against rank ordering of counties on the basis of simulation results. It argues towards using quartiles, which while requiring ranking presents gross rather than fine results, as well as for repeating simulations using different seeds and number of runs.

Population and Voter Turnout Aspects of North Carolina

In order to constructively respond to the question of the representativeness of boards of county commissioners, I will provide some information about the demographics of North Carolina population and voter turnout. For the purposes of this report, I will use data for 2016 unless otherwise stated.

The plot below shows the 2016 Black population percentage against the total population, by county. There were 34 counties with under 10% Black population. Those counties constitute 20% of the total population of the state. On the other hand, there were 0 counties with under 10% White population. Counties with a small population of any race are mathematically challenged to have a matching board composition.

The next plot looks at 2016 voter turnout. It shows the percentage of all the voters by county who self-reported as Black when their voter registration was recorded. There were 37 counties with under 10% Black of the total voter turnout. Those counties constitute 23% of the total voter turnout of the state. On the other hand, there were 0 counties with under 10% White of the total voter turnout. Counties with a small turnout of any race are mathematically challenged to have a matching board composition.

As a final step in this section, I show below the association between the Black population percentage and the Black voter turnout percentage, a combining of the two previous plots. There are a small number of counties that show appreciable deviations from equality, that is, the distance from a straight line of slope 1, passing through the origin. This infers that using either population or voter turnout in simulations should give similar results. It remains necessary to verify this.

Population and Voter Turnout Simulations

The basis for this current investigation of county commissioner representation is based on simulations. Each county board is described by the counts of American Indian, Black, and White commissioners provided by the NCACC. These three categories are the only ones provided in the NCACC data. I will assign a count of zero to the category Other when using in the NCACC data.

The board compositions are compared with combinatorial probabilities computed by simulation, using Census Bureau ACS population estimates. There are misalignments, or at least ambiguities, between the race categories provided in various data sources. I attempt to deal with that by reducing race categories to American Indian, Black, White, and a catchall of Other. As I have time for it, I will try to estimate the errors due to the different ways of tallying race. However, we are dealing with estimated population figures, and self-reported, category-limited, NCSBE and NCACC data. The best we can do is make estimates that are clearly documented. Of more substance, I will undertake to separate and compare the population and turnout simulations with the intention of detecting what significant differences there might be.

Any comparison of board composition to population is confronted with the small number of board members in each county. In 2016, there were 62 counties with five commissioners, 31 with seven, and 5 with more than seven. A county with five board members of two races necessarily has only 0:5, 1:4, or 2:3 composition. This means that if the county population is 50:50, the board proportions cannot match the county very well. The simulations will, of course, reflect this, and it will be necessary to utilize techniques other than simple comparisons to characterize representations.

This report uses a simulation of 10000 runs per county, based on the Census Bureau ACS 2016 population data. To start this, I will look at the behavior of the board simulations for some selected counties.

Consider first Anson and Washington. These are small counties with similar proportions of Black residents. Npct is the percentage of times that a particular board composition was generated. The results show what is mathematically necessary, namely that for Anson 4 Black, 3 White is as likely as 3 Black, 4 White, and similarly for Washington 3 and 2 is as likely as 2 and 3.

County Total AmIndPct BlackPct WhitePct OtherPct ncomm namin nafam nwhite
Anson 25883 0.3 48.7 48.0 2.9 7 0 4 3
Washington 12503 0.1 48.6 46.5 4.7 5 0 3 2


  1. Anson 7 Members
  1. Washington 5 Members
AmInd.1 Black.1 White.1 Other.1 Npct.1 AmInd.2 Black.2 White.2 Other.2 Npct.2
0 3 4 0 21.99 0 3 2 0 24.99
0 4 3 0 21.32 0 2 3 0 24.39
0 2 5 0 13.59 0 4 1 0 12.67
0 5 2 0 12.86 0 1 4 0 11.57
0 3 3 1 5.26 0 2 2 1 7.11
0 6 1 0 4.58 0 3 1 1 4.82
0 1 6 0 4.05 0 1 3 1 4.57
0 2 4 1 3.89 0 5 0 0 2.50
0 4 2 1 3.42 0 0 5 0 2.33
0 5 1 1 1.50 0 4 0 1 1.26
0 1 5 1 1.41 0 0 4 1 1.03
0 7 0 0 0.71 0 1 2 2 0.75
1 3 3 0 0.67 0 2 1 2 0.63
0 0 7 0 0.58 0 3 0 2 0.36
0 3 2 2 0.56 1 2 2 0 0.25
0 2 3 2 0.53 0 0 3 2 0.25
1 2 4 0 0.52 1 1 3 0 0.15
1 4 2 0 0.43 1 3 1 0 0.10
0 6 0 1 0.31 1 2 1 1 0.07
0 4 1 2 0.29 0 1 1 3 0.07
0 0 6 1 0.28 1 0 4 0 0.05
1 1 5 0 0.21 1 4 0 0 0.03
1 5 1 0 0.18 0 0 2 3 0.02
0 1 4 2 0.18 1 3 0 1 0.01
1 2 3 1 0.13 1 1 2 1 0.01
1 3 2 1 0.11 1 0 3 1 0.01
1 1 4 1 0.06 NA NA NA NA NA
0 0 5 2 0.05 NA NA NA NA NA
1 5 0 1 0.04 NA NA NA NA NA
1 4 1 1 0.04 NA NA NA NA NA
0 5 0 2 0.04 NA NA NA NA NA
0 3 1 3 0.04 NA NA NA NA NA
0 2 2 3 0.04 NA NA NA NA NA
1 2 2 2 0.03 NA NA NA NA NA
1 6 0 0 0.02 NA NA NA NA NA
2 3 2 0 0.01 NA NA NA NA NA
2 1 4 0 0.01 NA NA NA NA NA
2 0 5 0 0.01 NA NA NA NA NA
1 3 1 2 0.01 NA NA NA NA NA
1 1 3 2 0.01 NA NA NA NA NA
1 0 5 1 0.01 NA NA NA NA NA
0 4 0 3 0.01 NA NA NA NA NA
0 1 3 3 0.01 NA NA NA NA NA



Cumberland and Durham are both large. The following table shows the population-based simulation for these counties.

County Total AmIndPct BlackPct WhitePct OtherPct ncomm namin nafam nwhite
Cumberland 325841 1.5 36.9 51.0 10.7 7 0 3 4
Durham 294618 0.4 37.6 50.9 11.1 5 0 2 3


  1. Cumberland 7 Members
  1. Durham 5 Members
AmInd.1 Black.1 White.1 Other.1 Npct.1 AmInd.2 Black.2 White.2 Other.2 Npct.2
0 3 4 0 11.97 0 2 3 0 18.56
0 2 4 1 10.53 0 3 2 0 13.92
0 2 5 0 9.80 0 1 4 0 12.53
0 3 3 1 9.21 0 2 2 1 12.29
0 4 3 0 8.84 0 1 3 1 10.95
0 4 2 1 5.56 0 3 1 1 6.56
0 1 5 1 5.53 0 4 1 0 4.99
0 1 6 0 4.59 0 0 4 1 3.91
0 2 3 2 4.08 0 0 5 0 3.61
0 5 2 0 3.76 0 1 2 2 3.57
0 3 2 2 3.13 0 2 1 2 2.53
0 1 4 2 3.02 0 0 3 2 1.61
0 5 1 1 1.77 0 4 0 1 0.84
1 2 4 0 1.40 0 3 0 2 0.66
1 3 3 0 1.36 0 1 1 3 0.64
0 0 6 1 1.21 0 5 0 0 0.61
1 2 3 1 1.11 0 0 2 3 0.47
0 4 1 2 1.08 1 1 3 0 0.38
0 0 7 0 0.98 1 2 2 0 0.27
0 1 3 3 0.94 1 3 1 0 0.26
1 3 2 1 0.90 1 2 1 1 0.17
0 2 2 3 0.90 0 2 0 3 0.17
1 1 4 1 0.86 1 1 2 1 0.13
0 0 5 2 0.80 1 0 3 1 0.09
0 6 1 0 0.77 1 1 1 2 0.08
1 1 5 0 0.74 1 0 4 0 0.06
1 4 2 0 0.56 0 1 0 4 0.04
0 3 1 3 0.50 1 4 0 0 0.02
1 2 2 2 0.47 1 2 0 2 0.02
1 1 3 2 0.43 1 0 2 2 0.02
1 4 1 1 0.42 0 0 1 4 0.02
0 0 4 3 0.24 2 0 2 1 0.01
0 6 0 1 0.23 1 3 0 1 0.01
1 0 5 1 0.22 NA NA NA NA NA
1 5 1 0 0.18 NA NA NA NA NA
1 0 6 0 0.16 NA NA NA NA NA
0 5 0 2 0.16 NA NA NA NA NA
1 0 4 2 0.14 NA NA NA NA NA
1 3 1 2 0.13 NA NA NA NA NA
1 1 2 3 0.11 NA NA NA NA NA
0 1 2 4 0.10 NA NA NA NA NA
0 7 0 0 0.09 NA NA NA NA NA
2 3 2 0 0.08 NA NA NA NA NA
1 2 1 3 0.08 NA NA NA NA NA
0 2 1 4 0.08 NA NA NA NA NA
2 2 2 1 0.07 NA NA NA NA NA
2 2 3 0 0.07 NA NA NA NA NA
0 4 0 3 0.07 NA NA NA NA NA
0 0 3 4 0.07 NA NA NA NA NA
2 1 3 1 0.06 NA NA NA NA NA
1 5 0 1 0.06 NA NA NA NA NA
2 1 4 0 0.05 NA NA NA NA NA
1 6 0 0 0.04 NA NA NA NA NA
2 1 2 2 0.03 NA NA NA NA NA
2 0 5 0 0.03 NA NA NA NA NA
1 4 0 2 0.03 NA NA NA NA NA
1 0 3 3 0.03 NA NA NA NA NA
2 2 1 2 0.02 NA NA NA NA NA
2 0 4 1 0.02 NA NA NA NA NA
0 3 0 4 0.02 NA NA NA NA NA
0 2 0 5 0.02 NA NA NA NA NA
3 1 2 1 0.01 NA NA NA NA NA
3 1 3 0 0.01 NA NA NA NA NA
2 4 0 1 0.01 NA NA NA NA NA
2 4 1 0 0.01 NA NA NA NA NA
2 3 0 2 0.01 NA NA NA NA NA
2 0 3 2 0.01 NA NA NA NA NA
1 1 0 5 0.01 NA NA NA NA NA
1 1 1 4 0.01 NA NA NA NA NA
0 0 2 5 0.01 NA NA NA NA NA



Another duo of counties, distinguished by being the largest in the state, are Mecklenburg and Wake.

County Total AmIndPct BlackPct WhitePct OtherPct ncomm namin nafam nwhite
Mecklenburg 1011774 0.3 31.2 55.9 12.7 9 0 4 5
Wake 998576 0.3 20.6 67.1 12.0 7 0 2 5


  1. Mecklenburg 9 Members
  1. Wake 7 Members
AmInd.1 Black.1 White.1 Other.1 Npct.1 AmInd.2 Black.2 White.2 Other.2 Npct.2
0 3 5 1 10.85 0 1 5 1 14.47
0 2 6 1 9.10 0 1 6 0 12.75
0 4 4 1 7.41 0 2 5 0 12.53
0 3 6 0 7.35 0 2 4 1 10.64
0 2 5 2 6.44 0 0 6 1 7.91
0 4 5 0 6.41 0 1 4 2 6.58
0 3 4 2 6.41 0 3 4 0 6.42
0 2 7 0 5.82 0 0 7 0 5.70
0 1 7 1 4.88 0 3 3 1 4.57
0 1 6 2 3.94 0 0 5 2 3.91
0 5 3 1 3.69 0 2 3 2 3.57
0 5 4 0 3.53 0 4 3 0 1.83
0 4 3 2 3.07 0 1 3 3 1.36
0 1 8 0 2.61 0 0 4 3 1.24
0 2 4 3 2.37 0 3 2 2 1.15
0 1 5 3 1.75 0 4 2 1 0.90
0 3 3 3 1.63 0 2 2 3 0.72
0 6 3 0 1.23 0 5 2 0 0.40
0 0 8 1 1.13 1 2 4 0 0.37
0 5 2 2 1.11 1 1 4 1 0.36
0 0 7 2 1.08 1 2 3 1 0.28
0 6 2 1 0.88 0 1 2 4 0.25
0 4 2 3 0.69 1 0 6 0 0.24
0 0 9 0 0.53 1 1 5 0 0.22
0 0 6 3 0.50 1 0 5 1 0.22
0 2 3 4 0.40 0 0 3 4 0.20
0 3 2 4 0.36 0 4 1 2 0.16
0 1 4 4 0.36 0 5 1 1 0.15
0 7 2 0 0.34 0 3 1 3 0.13
1 2 5 1 0.33 1 0 4 2 0.12
1 3 5 0 0.30 1 3 3 0 0.11
1 3 4 1 0.29 1 1 3 2 0.08
1 2 6 0 0.28 1 3 2 1 0.06
1 2 4 2 0.26 1 2 2 2 0.06
0 5 1 3 0.23 0 6 1 0 0.05
1 3 3 2 0.21 0 0 2 5 0.05
0 6 1 2 0.20 1 1 2 3 0.04
0 7 1 1 0.18 1 4 2 0 0.03
1 4 4 0 0.16 0 4 0 3 0.03
1 1 6 1 0.16 0 2 1 4 0.03
0 0 5 4 0.12 2 1 4 0 0.02
1 4 3 1 0.11 1 4 1 1 0.02
1 1 5 2 0.11 1 0 3 3 0.02
1 1 7 0 0.11 0 5 0 2 0.02
1 4 2 2 0.10 2 1 3 1 0.01
1 1 4 3 0.09 2 0 3 2 0.01
0 2 2 5 0.09 0 2 0 5 0.01
1 5 2 1 0.07 NA NA NA NA NA
0 1 3 5 0.07 NA NA NA NA NA
1 5 3 0 0.06 NA NA NA NA NA
1 2 3 3 0.06 NA NA NA NA NA
0 8 1 0 0.06 NA NA NA NA NA
1 0 6 2 0.05 NA NA NA NA NA
1 0 7 1 0.05 NA NA NA NA NA
0 4 1 4 0.05 NA NA NA NA NA
0 7 0 2 0.04 NA NA NA NA NA
0 3 1 5 0.04 NA NA NA NA NA
0 6 0 3 0.03 NA NA NA NA NA
2 3 4 0 0.02 NA NA NA NA NA
1 6 2 0 0.02 NA NA NA NA NA
1 0 5 3 0.02 NA NA NA NA NA
0 2 1 6 0.02 NA NA NA NA NA
0 1 2 6 0.02 NA NA NA NA NA
0 0 4 5 0.02 NA NA NA NA NA
2 1 6 0 0.01 NA NA NA NA NA
2 0 3 4 0.01 NA NA NA NA NA
1 6 1 1 0.01 NA NA NA NA NA
1 5 1 2 0.01 NA NA NA NA NA
1 3 0 5 0.01 NA NA NA NA NA
1 3 2 3 0.01 NA NA NA NA NA
1 2 2 4 0.01 NA NA NA NA NA
1 0 8 0 0.01 NA NA NA NA NA
0 9 0 0 0.01 NA NA NA NA NA
0 5 0 4 0.01 NA NA NA NA NA


Clusters

Which counties had boards that did, or did not, well-represent the racial composition of the population? What objective criteria can we establish? I will use clustering, which is a mathematical approach to sweeping together simulated board compositions that have nearly the same probabilities. It is far from simple to compute clusters. Briefly, for this analysis, I will use the R package Ckmeans.1d.dp. Picture, then, a histogram of the percentage of the simulation runs that resulted in each board compositions, Npct. Now arrange this histogram in descending order by Npct. The computation starts with supposing that there are a small number k of clusters, perhaps three to five. It proceeds to find k (or fewer) positions for the Npct such that the within cluster sum of squares to each cluster mean (withinss) is minimized. This takes a lot of work and I depend entirely on the sagacity of the authors of that package. I will number the clusters from left to right, that is, cluster 1 will correspond to the grouping of the highest values for Npct. Not all data is amenable to cluster analysis - the flatter the distribution of the variable of interest, the less well can it be said to have clusters. The Appendix pursues withinss at more length.

I will use the clusters computed for the board composition simulations based on population estimates of all the counties. Using both three and five cluster targets, I will determine the cluster number for the actual 2016 board compositions. I have already mentioned that there were 34 counties with under 10% Black population. It seems reasonable to expect that there would be good matches for these counties since there are few choices other than all White commissioners. In light of this I will note counties as being over or under 10% Black population proportion when that seems useful.

For five clusters the fit to the first cluster, where the actual board composition matches well with the population, we have:

over10 Cluster N
NO 1 33
NO 2 1
YES 1 38
YES 2 19
YES 3 5
YES 4 2
YES 5 2



Three clusters shows much the same. Having this smaller number of clusters might be a better aid to assessing comparability. I will continue this report using the three cluster data.

over10 Cluster N
NO 1 33
NO 2 1
YES 1 50
YES 2 11
YES 3 5



It is evident that there are 83 counties for the three cluster computation and 71 for the five cluster configuration whose 2016 board compositions match the population simulation cluster 1. That is, the simulation appears to announce that at least 71% of the counties had representative board compositions.

Which counties with over 10% Black population are in the clusters? I will provide this information as two separate lists, one for those in cluster 1, another for those in clusters 2 and 3. The following table shows the counties with over 10% Black population that are in the most representative cluster. There are some oddities in this list. For instance, Robeson County is included even though Npct (the percentage of times that the simulation resulted in the actual board composition) is only 4.72%. An interpretation in the case of Robeson is that, compared to many other counties, there are a large number of likely board compositions. Similar remarks can be made about other counties with low Npct.

These are the 50 counties in 2016 with over 10% Black population that are in cluster 1, the most representative of the three clusters:

County n_clus ncomm AmInd Black White Other Npct
Anson 1 7 0 4 3 0 21.32
Beaufort 1 7 0 2 5 0 25.04
Bladen 1 9 0 3 6 0 13.16
Brunswick 1 5 0 0 5 0 40.45
Cabarrus 1 5 0 0 5 0 21.77
Camden 1 5 0 0 5 0 39.04
Caswell 1 7 0 2 5 0 21.40
Chowan 1 7 0 2 5 0 23.65
Craven 1 7 0 2 5 0 16.70
Cumberland 1 7 0 3 4 0 11.97
Duplin 1 5 0 2 3 0 16.67
Durham 1 5 0 2 3 0 18.56
Edgecombe 1 7 0 4 3 0 21.27
Forsyth 1 7 0 2 5 0 18.68
Franklin 1 7 0 2 5 0 19.21
Gates 1 5 0 1 4 0 27.06
Granville 1 7 0 2 5 0 16.66
Greene 1 5 0 2 3 0 23.29
Guilford 1 9 0 3 6 0 10.23
Halifax 1 6 0 3 3 0 19.09
Harnett 1 5 0 1 4 0 21.81
Hertford 1 5 0 4 1 0 20.85
Lee 1 7 0 1 6 0 15.72
Lenoir 1 7 0 2 5 0 15.36
Martin 1 5 0 2 3 0 30.14
Montgomery 1 5 0 0 5 0 26.20
Moore 1 5 0 0 5 0 39.07
Nash 1 7 0 2 5 0 13.55
New Hanover 1 5 0 1 4 0 30.63
Onslow 1 5 0 0 5 0 23.31
Orange 1 7 0 1 6 0 14.85
Pamlico 1 7 0 1 6 0 23.45
Pasquotank 1 7 0 2 5 0 18.88
Pender 1 5 0 0 5 0 26.37
Perquimans 1 6 0 2 4 0 26.20
Person 1 5 0 1 4 0 29.84
Pitt 1 9 0 3 6 0 13.29
Robeson 1 8 3 2 3 0 4.72
Rockingham 1 5 0 0 5 0 25.59
Rowan 1 5 0 0 5 0 29.66
Rutherford 1 5 0 0 5 0 45.88
Sampson 1 5 0 2 3 0 15.41
Scotland 1 7 0 3 4 0 8.63
Stanly 1 7 0 0 7 0 31.38
Union 1 5 0 0 5 0 36.55
Vance 1 7 0 4 3 0 18.17
Wake 1 7 0 2 5 0 12.53
Washington 1 5 0 3 2 0 24.99
Wayne 1 7 0 2 5 0 15.36
Wilson 1 7 0 3 4 0 13.54



Here are the 16 counties with over 10% Black population that are in clusters 2 and 3, the least representative of the three clusters:

County n_clus ncomm AmInd Black White Other Npct
Alamance 2 5 0 0 5 0 17.46
Bertie 2 5 0 2 3 0 17.48
Chatham 2 5 0 1 4 0 25.34
Cleveland 3 5 1 0 4 0 0.45
Columbus 2 7 0 1 6 0 11.86
Gaston 2 7 0 0 7 0 15.99
Hoke 3 5 1 3 1 0 2.69
Hyde 2 5 0 0 5 0 13.42
Iredell 2 5 0 1 4 0 27.62
Johnston 2 7 0 0 7 0 17.88
Jones 2 5 0 0 5 0 12.49
Mecklenburg 2 9 0 4 5 0 6.41
Northampton 3 5 0 5 0 0 6.32
Richmond 3 7 0 0 7 0 4.19
Tyrrell 2 5 0 1 4 0 17.80
Warren 3 5 0 5 0 0 3.10



Here are the counts of counties by number of simulated board compositions in cluster 1, first for the three cluster categorization:

Configs. in Cluster 1 N
1 52
2 37
3 3
4 2
5 5
6 1



Here for the five cluster categorization:

Configs. in Cluster 1 N
1 83
2 15
3 2


A Diversity Measure for Counties: Theil’s Entropy Index

Analysis of representativeness may benefit from use of an alternative to the combinatorial approach, that of a quantitative measure of diversity, one used by economists and social scientists. The measure I will use is called Theil’s Entropy Index, which comes from information theory. The Index measures diversity but in a way that does not distinguish between specific population groups. For example, in our case populations are composed of the four race categories American Indian, Black, White, and Other. The index would have the same value for 20% Black and 80% White, compared to 80% Black and 20% White - it measures diversity not matter how it is achieved. Theil’s Entropy Index, called H in this report, is computed as described in the next paragraph. I will do this for the board, and also for the county populations. These two indexes can then be compared.

Mathematically, the calculation looks like this: let pi be the proportion of race i, then H is the sum of \(p_i\cdot ln(1/p_i)\). If there are four categories and only one is present, then \(H=1\cdot ln(1)=0\). This is the least diverse, and has the lowest H. If the proportions are (0,0,0.2,0.8), then \(H=0.2\cdot ln(1/0.2)+0.8\cdot ln(1/0.8)\sim 0.50\). An even split between only two races (0,0,0.5,0.5) would result in \(H=2\cdot (0.5)\cdot ln(1/0.5)\sim 0.69\). If all are present equally, then \(H=4\cdot (1/4)\cdot ln(1/0.25)\sim 1.39\). If there are N categories, H varies between 0 for the least diversity to ln(N) for the most uniform, which can be called the most diverse. In our case, N=4, so the maximum H is 1.39.

Counties collect in more-or-less horizontal lines because boards are small in size and, accordingly, there are only a few realizable values for their diversity index. Counties with boards that have a zero diversity index have members of one race only. Speaking in general terms, it would be desirable to have board diversity comparable to that of the county population. This would put the data points in the next plots near the diagonal line, where the county and the actual board diversities would be the same.

The next plot utilizes data for all one hundred counties. Even though the diversity measure is entirely independent of the clustering we used previously, it may be of interest to identify the counties by which cluster they were in. That is what is embodied in this plot.

The 52 counties with Board Diversity Index of zero (that is, where the board is composed of members of a single race category) are shown below in order by Hcty, the population Diversity Index, with their populations and 2016 board compositions. Since these counties have boards composed of persons from one race only (the board H is zero), the further from zero the Hcty, the less representative the board.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite
Clay 10730 0.0 0.4 99.2 0.4 0.051 5 0 0 5
Mitchell 15263 0.6 0.4 96.9 2.0 0.163 5 0 0 5
Yancey 17599 0.4 1.2 96.5 1.9 0.183 5 0 0 5
Madison 21130 0.2 1.9 96.1 1.8 0.197 5 0 0 5
Haywood 59577 0.3 1.1 95.9 2.7 0.204 5 0 0 5
Ashe 26992 0.3 0.7 93.9 5.0 0.264 5 0 0 5
Watauga 52745 0.3 1.2 94.0 4.5 0.268 5 0 0 5
Cherokee 27226 1.5 1.4 93.7 3.4 0.297 5 0 0 5
Stokes 46453 0.6 4.2 93.4 1.9 0.300 5 0 0 5
Macon 33991 0.5 1.2 92.6 5.8 0.313 5 0 0 5
Surry 72767 0.4 3.7 92.0 3.9 0.346 5 0 0 5
Avery 17633 0.5 3.7 91.9 3.9 0.352 5 0 0 5
Yadkin 37819 0.3 3.4 91.5 4.8 0.359 5 0 0 5
Dare 35187 0.3 2.0 91.1 6.7 0.360 7 0 0 7
Henderson 110905 0.2 3.1 91.1 5.5 0.366 5 0 0 5
Polk 20324 0.2 5.3 91.2 3.3 0.366 5 0 0 5
Wilkes 68888 0.2 4.3 91.2 4.4 0.368 5 0 0 5
Alleghany 10868 1.6 2.4 91.4 4.6 0.378 5 0 0 5
McDowell 45013 0.5 4.0 91.0 4.4 0.381 5 0 0 5
Currituck 24864 0.6 6.2 90.5 2.8 0.392 7 0 0 7
Transylvania 33062 0.4 3.9 90.4 5.4 0.395 5 0 0 5
Caldwell 81623 0.5 4.9 89.5 5.1 0.426 5 0 0 5
Graham 8651 8.1 0.4 88.8 2.7 0.429 5 0 0 5
Davie 41568 0.1 6.3 88.6 5.0 0.435 5 0 0 5
Carteret 68537 0.4 6.1 88.9 4.7 0.439 7 0 0 7
Alexander 37211 0.3 5.8 88.7 5.2 0.443 5 0 0 5
Lincoln 79783 0.2 5.4 88.4 6.0 0.449 5 0 0 5
Davidson 164058 0.4 9.0 86.5 4.1 0.496 7 0 0 7
Randolph 142588 0.4 6.1 86.6 6.8 0.503 5 0 0 5
Rutherford 66701 0.5 10.3 85.5 3.7 0.517 5 0 0 5
Stanly 60610 0.3 10.5 84.5 4.7 0.541 7 0 0 7
Camden 10228 0.2 14.2 82.6 3.0 0.553 5 0 0 5
Burke 89082 0.5 6.2 84.4 9.0 0.558 5 0 0 5
Brunswick 119167 0.4 10.6 83.5 5.5 0.571 5 0 0 5
Moore 93070 0.7 12.5 82.8 4.0 0.580 5 0 0 5
Union 217614 0.3 11.6 81.6 6.4 0.611 5 0 0 5
Jackson 41227 8.5 3.1 83.5 4.9 0.616 5 0 0 5
Catawba 155461 0.3 8.6 79.7 11.5 0.657 5 0 0 5
Rowan 138694 0.2 16.1 78.1 5.5 0.661 5 0 0 5
Hyde 5629 0.2 33.0 66.5 0.4 0.669 5 0 0 5
Montgomery 27475 0.3 18.8 76.6 4.3 0.669 5 0 0 5
Johnston 182155 0.5 15.3 78.2 6.0 0.676 7 0 0 7
Pender 56358 0.4 16.4 76.6 6.6 0.704 5 0 0 5
Rockingham 91898 0.5 18.5 75.8 5.2 0.704 5 0 0 5
Gaston 211753 0.4 15.4 76.8 7.5 0.706 7 0 0 7
Cabarrus 192296 0.3 16.7 73.9 9.1 0.758 5 0 0 5
Onslow 185755 0.5 15.0 74.3 10.2 0.765 5 0 0 5
Jones 10074 0.3 30.6 65.9 3.2 0.768 5 0 0 5
Northampton 20628 0.5 57.4 39.4 2.7 0.809 5 0 5 0
Alamance 156372 0.4 18.6 70.7 10.3 0.814 5 0 0 5
Richmond 45710 2.0 31.7 62.9 3.4 0.850 7 0 0 7
Warren 20324 4.8 50.8 39.6 4.8 1.002 5 0 5 0

Combining Simulations and Diversity Indexes

The two methodologies discussed above, simulation and diversity index, are independent of each other. That is to say that, while that use the same data, their computations have nothing in common. In this section I will combine them in what I feel is a reasonable way and make some interesting observations.

Plots

The following plot shows the counties that were in cluster 1, where the actual board result was a likely result of the population simulation.

The next plot shows the counties that were in cluster 2 or 3, where the actual board result was less likely a result of the population simulation.

Tables

The 44 counties with Board Diversity Index of zero (that is, where the board is composed of members of a single race category) that are in cluster 1 are shown below in Hcty order, with their populations and 2016 board compositions. Since these counties have boards composed of persons from one race only (the board H is zero), the further from zero the Hcty, the population Diversity Index, the less representative the board.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite
Clay 10730 0.0 0.4 99.2 0.4 0.051 5 0 0 5
Mitchell 15263 0.6 0.4 96.9 2.0 0.163 5 0 0 5
Yancey 17599 0.4 1.2 96.5 1.9 0.183 5 0 0 5
Madison 21130 0.2 1.9 96.1 1.8 0.197 5 0 0 5
Haywood 59577 0.3 1.1 95.9 2.7 0.204 5 0 0 5
Ashe 26992 0.3 0.7 93.9 5.0 0.264 5 0 0 5
Watauga 52745 0.3 1.2 94.0 4.5 0.268 5 0 0 5
Cherokee 27226 1.5 1.4 93.7 3.4 0.297 5 0 0 5
Stokes 46453 0.6 4.2 93.4 1.9 0.300 5 0 0 5
Macon 33991 0.5 1.2 92.6 5.8 0.313 5 0 0 5
Surry 72767 0.4 3.7 92.0 3.9 0.346 5 0 0 5
Avery 17633 0.5 3.7 91.9 3.9 0.352 5 0 0 5
Yadkin 37819 0.3 3.4 91.5 4.8 0.359 5 0 0 5
Dare 35187 0.3 2.0 91.1 6.7 0.360 7 0 0 7
Henderson 110905 0.2 3.1 91.1 5.5 0.366 5 0 0 5
Polk 20324 0.2 5.3 91.2 3.3 0.366 5 0 0 5
Wilkes 68888 0.2 4.3 91.2 4.4 0.368 5 0 0 5
Alleghany 10868 1.6 2.4 91.4 4.6 0.378 5 0 0 5
McDowell 45013 0.5 4.0 91.0 4.4 0.381 5 0 0 5
Currituck 24864 0.6 6.2 90.5 2.8 0.392 7 0 0 7
Transylvania 33062 0.4 3.9 90.4 5.4 0.395 5 0 0 5
Caldwell 81623 0.5 4.9 89.5 5.1 0.426 5 0 0 5
Graham 8651 8.1 0.4 88.8 2.7 0.429 5 0 0 5
Davie 41568 0.1 6.3 88.6 5.0 0.435 5 0 0 5
Carteret 68537 0.4 6.1 88.9 4.7 0.439 7 0 0 7
Alexander 37211 0.3 5.8 88.7 5.2 0.443 5 0 0 5
Lincoln 79783 0.2 5.4 88.4 6.0 0.449 5 0 0 5
Davidson 164058 0.4 9.0 86.5 4.1 0.496 7 0 0 7
Randolph 142588 0.4 6.1 86.6 6.8 0.503 5 0 0 5
Rutherford 66701 0.5 10.3 85.5 3.7 0.517 5 0 0 5
Stanly 60610 0.3 10.5 84.5 4.7 0.541 7 0 0 7
Camden 10228 0.2 14.2 82.6 3.0 0.553 5 0 0 5
Burke 89082 0.5 6.2 84.4 9.0 0.558 5 0 0 5
Brunswick 119167 0.4 10.6 83.5 5.5 0.571 5 0 0 5
Moore 93070 0.7 12.5 82.8 4.0 0.580 5 0 0 5
Union 217614 0.3 11.6 81.6 6.4 0.611 5 0 0 5
Jackson 41227 8.5 3.1 83.5 4.9 0.616 5 0 0 5
Catawba 155461 0.3 8.6 79.7 11.5 0.657 5 0 0 5
Rowan 138694 0.2 16.1 78.1 5.5 0.661 5 0 0 5
Montgomery 27475 0.3 18.8 76.6 4.3 0.669 5 0 0 5
Pender 56358 0.4 16.4 76.6 6.6 0.704 5 0 0 5
Rockingham 91898 0.5 18.5 75.8 5.2 0.704 5 0 0 5
Cabarrus 192296 0.3 16.7 73.9 9.1 0.758 5 0 0 5
Onslow 185755 0.5 15.0 74.3 10.2 0.765 5 0 0 5


The 8 counties with Board Diversity Index of zero that are in clusters 2 or 3 are shown below in Hcty order, with their populations and 2016 board compositions. Since they all have boards composed of persons of a single race, and they were in cluster 2 or 3, where the board composition was an unlikely consequence of their population proportions, they may all be considered unrepresentative. These counties merit further study.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite
Hyde 5629 0.2 33.0 66.5 0.4 0.669 5 0 0 5
Johnston 182155 0.5 15.3 78.2 6.0 0.676 7 0 0 7
Gaston 211753 0.4 15.4 76.8 7.5 0.706 7 0 0 7
Jones 10074 0.3 30.6 65.9 3.2 0.768 5 0 0 5
Northampton 20628 0.5 57.4 39.4 2.7 0.809 5 0 5 0
Alamance 156372 0.4 18.6 70.7 10.3 0.814 5 0 0 5
Richmond 45710 2.0 31.7 62.9 3.4 0.850 7 0 0 7
Warren 20324 4.8 50.8 39.6 4.8 1.002 5 0 5 0


The remaining 9 counties in this plot are in the following list. They are arranged by the difference between the county population H and the board H, in ascending order. These counties have boards composed of more than one race, and are in cluster 2 or 3, the less likely simulation compositions. These counties are of less pronounced representation concerns than those discussed immediately above but may merit further study.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite Hboard Hdiff
Buncombe 250112 0.4 6.3 88.8 4.5 0.440 7 0 1 6 0.410 0.030
Bertie 20324 0.6 62.0 36.0 1.4 0.754 5 0 2 3 0.673 0.081
Iredell 167493 0.4 12.3 81.6 5.7 0.611 5 0 1 4 0.500 0.111
Chatham 68778 0.3 11.9 80.4 7.4 0.638 5 0 1 4 0.500 0.137
Cleveland 97113 0.2 20.8 75.5 3.5 0.671 5 1 0 4 0.500 0.170
Hoke 51853 8.3 33.3 45.8 12.6 1.191 5 1 3 1 0.950 0.241
Mecklenburg 1011774 0.3 31.2 55.9 12.7 0.968 9 0 4 5 0.687 0.281
Tyrrell 4128 2.1 36.6 55.8 5.5 0.934 5 0 1 4 0.500 0.434
Columbus 57015 3.7 30.9 61.6 3.8 0.907 7 0 1 6 0.410 0.497


Appendix A: Comments on the American Indian Population

In 2016, 4 counties reported American Indian board members. The following table shows characteristics of these counties. By way of comparison, the median American Indian population in 2016 was 282.5 and UH, the “upper hinge” (one-and-a-half times the interquartile distance above the median), was 736.5. There were 25 counties with American Indian populations above the upper hinge.

County Ncomm AmInd Black White total_AmInd total_Black total_White above_UH
Cleveland 5 1 0 4 221 20151 73303 No
Hoke 5 1 3 1 4281 17275 23751 Yes
Robeson 8 3 2 3 52120 32599 39500 Yes
Swain 5 1 0 4 3952 186 9143 Yes
Table 1: (above) Counties with American Indian Commissioners 2016

The next table shows some characteristics of the 10 counties with the highest American Indian population.

County Total AmInd Black White Other N_AmInd
Halifax 52849 1901 27527 21187 2234 0
Columbus 57015 2111 17625 35133 2146 0
Guilford 511815 2297 171837 288612 49069 0
Mecklenburg 1011774 3181 315272 565183 128138 0
Wake 998576 3405 205682 669687 119802 0
Jackson 41227 3504 1274 34411 2038 0
Scotland 35711 3777 13730 16249 1955 0
Swain 14234 3952 186 9143 953 1
Hoke 51853 4281 17275 23751 6546 1
Cumberland 325841 4738 120092 166292 34719 0
Robeson 134576 52120 32599 39500 10357 3
Table 2: (above) Counties with Highest American Indian Population 2016

Conditioning on American Indian Voter Turnout

In this section I make similar observations about American Indian representation, but looking at voter turnout instead of population estimates.

The following table shows voter turnout characteristics of the counties that had American Indian board members. By way of comparison, the median American Indian voter turnout in 2016 was 57.5 and UHT, the “upper hinge” (one-and-a-half times the interquartile distance above the median), was 193.5.

County Ncomm AmInd Black White total_AmInd total_Black total_White above_UHT
Cleveland 5 1 0 4 52 9269 34113 No
Hoke 5 1 3 1 1028 7675 8199 Yes
Robeson 8 3 2 3 12558 12212 14759 Yes
Swain 5 1 0 4 859 34 5188 Yes
Table 3: (above) American Indian Voter Turnout 2016

The next table shows some characteristics of the 10 counties with the highest American Indian 2016 turnout.

County Total AmInd Black White Other N_AmInd
Columbus 23804 538 6932 15873 461 0
Guilford 258714 603 84874 155460 17777 0
Halifax 25205 737 13244 10475 749 0
Jackson 18872 752 432 16672 1016 0
Scotland 13988 764 5633 7084 507 0
Swain 6202 859 34 5188 121 1
Hoke 18289 1028 7675 8199 1387 1
Mecklenburg 475593 1155 147732 281907 44799 0
Wake 531248 1202 96385 368296 65365 0
Cumberland 128007 1207 53965 59561 13274 0
Robeson 41137 12558 12212 14759 1608 3
Table 4: (above) Counties with Highest American Indian Turnout 2016

Observations on American Indian Representation

Cleveland county, with a very small American Indian population, had one commissioner from that race category in 2016. Since there are five commissioners, the representation was twenty percent as compared to the 0.2% population proportion. The proportion of American Indian voters was 0.1%. The disproportion of board membership is an expression of the small number of commissioners.

Robeson county had eight commissioners with three being American Indian in 2016. This was 38% of the board, while the population proportion was 39%. The proportion of American Indian voters was 30.5%. The difference between five and eight commissioners moves the proportions from multiples of 20% to multiples of 12.5%, which can have a substantial impact on representation proportions.

Appendix B: Characterization of the Clusters

Clustering makes most sense if the underlying proportion data has features. The inference here is that the county populations that are more or less uniform would result in larger numbers of board compositions that are likely, that is, the number of board compositions that constitute a cluster. If cluster 1, which contains the most likely board compositions, contains many individual instances, the uniqueness of the clustering would be less than if it contained fewer instances. The clustering computation yields a measure, the withinss, the sum of squares of distances from a centroid, that can be used to make comparisons of this uniqueness.

I have scaled the withinss by dividing by the ratio of the county population to the minimum of all populations. I present in the following plot the log of the scaled withinss. The counties grouped horizontally at the bottom all have a cluster 1 with only one member Npct, that is, the simulation results in a unique match to the actual board. Counties toward the top of the plot, with cluster 1 having the highest scaled withinss, should be associated with counties that have greater numbers of simulated board compositions in cluster 1.



Here is a list of the cluster 1 counties arranged in descending order by the scaled withinss. Larger values correspond to more spread out clusters, that is, clusters that contain more potential board configurations.

County Total withinss withinss_scaled
Montgomery 27475 758930673.1 19.291819
Person 39196 433563701.8 18.376649
Stanly 60610 400079817.9 17.860390
New Hanover 216430 354511369.0 16.466659
Rockingham 91898 354150218.7 17.322227
Perquimans 13470 310446183.2 19.110731
Duplin 59121 230630277.2 17.334415
Lenoir 58343 226675214.3 17.330364
Hertford 24285 123382449.1 17.598616
Sampson 63713 119437550.4 16.601591
Beaufort 47513 113777391.9 16.846426
Caswell 23094 109883778.8 17.533036
Edgecombe 54669 106686999.6 16.641788
Wayne 124447 95301121.3 15.706347
Nash 94385 94710716.3 15.976631
Swain 14234 92049839.0 17.839882
Wake 998576 90782829.6 13.575325
Wilson 81617 90016891.3 16.071145
Cabarrus 192296 82081670.2 15.121864
Chowan 14556 79830637.5 17.675090
Guilford 511815 70553071.2 13.991587
Forsyth 364691 68211239.0 14.296744
Franklin 62989 65647412.4 16.014524
Cumberland 325841 65589561.0 14.370192
Pender 56358 55224337.2 15.952865
Vance 44508 55027288.8 16.185346
Lee 59540 51712257.2 15.832232
Orange 139807 40833735.4 14.742431
Granville 58341 39785599.0 15.590385
Scotland 35711 32759727.3 15.886927
Pasquotank 39909 19724694.5 15.268455
Halifax 52849 17248247.0 14.853457
Pitt 175150 12989817.3 13.371709
Craven 104190 12652641.4 13.864835
Anson 25883 4859301.6 14.300494
Washington 12503 4443543.9 14.938669
Bladen 34454 4180059.1 13.863886
Robeson 134576 3294581.5 12.263336
Gates 11615 2887076.9 14.581133
Onslow 185755 561427.4 10.171484
Rowan 138694 148549.6 9.134079
Alexander 37211 0.0 1.000000
Alleghany 10868 0.0 1.000000
Ashe 26992 0.0 1.000000
Avery 17633 0.0 1.000000
Brunswick 119167 0.0 1.000000
Burke 89082 0.0 1.000000
Caldwell 81623 0.0 1.000000
Camden 10228 0.0 1.000000
Carteret 68537 0.0 1.000000
Catawba 155461 0.0 1.000000
Cherokee 27226 0.0 1.000000
Clay 10730 0.0 1.000000
Currituck 24864 0.0 1.000000
Dare 35187 0.0 1.000000
Davidson 164058 0.0 1.000000
Davie 41568 0.0 1.000000
Durham 294618 0.0 1.000000
Graham 8651 0.0 1.000000
Greene 21241 0.0 1.000000
Harnett 126620 0.0 1.000000
Haywood 59577 0.0 1.000000
Henderson 110905 0.0 1.000000
Jackson 41227 0.0 1.000000
Lincoln 79783 0.0 1.000000
McDowell 45013 0.0 1.000000
Macon 33991 0.0 1.000000
Madison 21130 0.0 1.000000
Martin 23510 0.0 1.000000
Mitchell 15263 0.0 1.000000
Moore 93070 0.0 1.000000
Pamlico 12892 0.0 1.000000
Polk 20324 0.0 1.000000
Randolph 142588 0.0 1.000000
Rutherford 66701 0.0 1.000000
Stokes 46453 0.0 1.000000
Surry 72767 0.0 1.000000
Transylvania 33062 0.0 1.000000
Union 217614 0.0 1.000000
Watauga 52745 0.0 1.000000
Wilkes 68888 0.0 1.000000
Yadkin 37819 0.0 1.000000
Yancey 17599 0.0 1.000000

Appendix C: Supplement to the Entropy Index Analysis

I have rearranged the diversity indexes in the following plot. This shows the difference between the county and the board indexes. The numeric value of this difference has no useful interpretation. The significance is in suggesting which counties to pursue further.

Appendix D: Quick List of County Populations as ACS Estimates

This is for 2016.

County FIPS3 Total AmInd Black White Other AmIndPct BlackPct WhitePct OtherPct Hcty
Alamance 001 156372 621 29039 110548 16164 0.4 18.6 70.7 10.3 0.8144
Alexander 003 37211 114 2142 33005 1950 0.3 5.8 88.7 5.2 0.4430
Alleghany 005 10868 170 262 9936 500 1.6 2.4 91.4 4.6 0.3785
Anson 007 25883 86 12612 12423 762 0.3 48.7 48.0 2.9 0.8254
Ashe 009 26992 92 193 25354 1353 0.3 0.7 93.9 5.0 0.2635
Avery 011 17633 86 655 16209 683 0.5 3.7 91.9 3.9 0.3516
Beaufort 013 47513 54 12331 33458 1670 0.1 26.0 70.4 3.5 0.7224
Bertie 015 20324 127 12608 7313 276 0.6 62.0 36.0 1.4 0.7541
Bladen 017 34454 817 12086 19831 1720 2.4 35.1 57.6 5.0 0.9238
Brunswick 019 119167 506 12589 99521 6551 0.4 10.6 83.5 5.5 0.5706
Buncombe 021 250112 886 15713 222134 11379 0.4 6.3 88.8 4.5 0.4398
Burke 023 89082 459 5483 75155 7985 0.5 6.2 84.4 9.0 0.5584
Cabarrus 025 192296 568 32188 142064 17476 0.3 16.7 73.9 9.1 0.7580
Caldwell 027 81623 442 3998 73059 4124 0.5 4.9 89.5 5.1 0.4260
Camden 029 10228 23 1450 8452 303 0.2 14.2 82.6 3.0 0.5525
Carteret 031 68537 258 4157 60921 3201 0.4 6.1 88.9 4.7 0.4388
Caswell 033 23094 41 7518 14408 1127 0.2 32.6 62.4 4.9 0.8183
Catawba 035 155461 443 13304 123873 17841 0.3 8.6 79.7 11.5 0.6565
Chatham 037 68778 185 8218 55295 5080 0.3 11.9 80.4 7.4 0.6376
Cherokee 039 27226 398 375 25518 935 1.5 1.4 93.7 3.4 0.2973
Chowan 041 14556 178 4889 9163 326 1.2 33.6 62.9 2.2 0.7967
Clay 043 10730 0 45 10646 39 0.0 0.4 99.2 0.4 0.0512
Cleveland 045 97113 221 20151 73303 3438 0.2 20.8 75.5 3.5 0.6708
Columbus 047 57015 2111 17625 35133 2146 3.7 30.9 61.6 3.8 0.9068
Craven 049 104190 699 22365 73456 7670 0.7 21.5 70.5 7.4 0.8023
Cumberland 051 325841 4738 120092 166292 34719 1.5 36.9 51.0 10.7 1.0113
Currituck 053 24864 140 1550 22490 684 0.6 6.2 90.5 2.8 0.3918
Dare 055 35187 94 707 32040 2346 0.3 2.0 91.1 6.7 0.3602
Davidson 057 164058 669 14750 141859 6780 0.4 9.0 86.5 4.1 0.4964
Davie 059 41568 21 2635 36842 2070 0.1 6.3 88.6 5.0 0.4350
Duplin 061 59121 114 14724 38153 6130 0.2 24.9 64.5 10.4 0.8759
Durham 063 294618 1091 110777 150067 32683 0.4 37.6 50.9 11.1 0.9761
Edgecombe 065 54669 216 30998 21006 2449 0.4 56.7 38.4 4.5 0.8502
Forsyth 067 364691 780 95187 242803 25921 0.2 26.1 66.6 7.1 0.8225
Franklin 069 62989 808 16230 42412 3539 1.3 25.8 67.3 5.6 0.8334
Gaston 071 211753 824 32627 162526 15776 0.4 15.4 76.8 7.5 0.7063
Gates 073 11615 96 3837 7363 319 0.8 33.0 63.4 2.7 0.7932
Graham 075 8651 704 34 7681 232 8.1 0.4 88.8 2.7 0.4286
Granville 077 58341 356 17960 35739 4286 0.6 30.8 61.3 7.3 0.8858
Greene 079 21241 102 7554 11960 1625 0.5 35.6 56.3 7.7 0.9134
Guilford 081 511815 2297 171837 288612 49069 0.4 33.6 56.4 9.6 0.9385
Halifax 083 52849 1901 27527 21187 2234 3.6 52.1 40.1 4.2 0.9595
Harnett 085 126620 1137 26921 85578 12984 0.9 21.3 67.6 10.3 0.8698
Haywood 087 59577 167 637 57137 1636 0.3 1.1 95.9 2.7 0.2038
Henderson 089 110905 219 3488 101051 6147 0.2 3.1 91.1 5.5 0.3662
Hertford 091 24285 260 14144 8572 1309 1.1 58.2 35.3 5.4 0.8884
Hoke 093 51853 4281 17275 23751 6546 8.3 33.3 45.8 12.6 1.1910
Hyde 095 5629 10 1855 3743 21 0.2 33.0 66.5 0.4 0.6692
Iredell 097 167493 749 20622 136625 9497 0.4 12.3 81.6 5.7 0.6110
Jackson 099 41227 3504 1274 34411 2038 8.5 3.1 83.5 4.9 0.6165
Johnston 101 182155 962 27836 142427 10930 0.5 15.3 78.2 6.0 0.6759
Jones 103 10074 35 3080 6634 325 0.3 30.6 65.9 3.2 0.7679
Lee 105 59540 405 11332 41679 6124 0.7 19.0 70.0 10.3 0.8333
Lenoir 107 58343 209 22838 32054 3242 0.4 39.1 54.9 5.6 0.8770
Lincoln 109 79783 188 4271 70542 4782 0.2 5.4 88.4 6.0 0.4485
McDowell 111 45013 238 1804 40968 2003 0.5 4.0 91.0 4.4 0.3808
Macon 113 33991 161 391 31469 1970 0.5 1.2 92.6 5.8 0.3132
Madison 115 21130 36 407 20310 377 0.2 1.9 96.1 1.8 0.1968
Martin 117 23510 81 10162 12711 556 0.3 43.2 54.1 2.4 0.8031
Mecklenburg 119 1011774 3181 315272 565183 128138 0.3 31.2 55.9 12.7 0.9684
Mitchell 121 15263 92 62 14797 312 0.6 0.4 96.9 2.0 0.1628
Montgomery 123 27475 75 5166 21057 1177 0.3 18.8 76.6 4.3 0.6692
Moore 125 93070 652 11654 77031 3733 0.7 12.5 82.8 4.0 0.5805
Nash 127 94385 624 36659 50234 6868 0.7 38.8 53.2 7.3 0.9269
New Hanover 129 216430 636 30589 175310 9895 0.3 14.1 81.0 4.6 0.6054
Northampton 131 20628 104 11843 8133 548 0.5 57.4 39.4 2.7 0.8086
Onslow 133 185755 937 27888 138029 18901 0.5 15.0 74.3 10.2 0.7646
Orange 135 139807 709 16010 105093 17995 0.5 11.5 75.2 12.9 0.7534
Pamlico 137 12892 148 2374 9722 648 1.1 18.4 75.4 5.0 0.7260
Pasquotank 139 39909 77 14580 23440 1812 0.2 36.5 58.7 4.5 0.8329
Pender 141 56358 243 9219 43164 3732 0.4 16.4 76.6 6.6 0.7037
Perquimans 143 13470 20 3296 9880 274 0.1 24.5 73.3 2.0 0.6607
Person 145 39196 361 10551 26918 1366 0.9 26.9 68.7 3.5 0.7715
Pitt 147 175150 515 60578 102061 11996 0.3 34.6 58.3 6.8 0.8827
Polk 149 20324 45 1084 18530 665 0.2 5.3 91.2 3.3 0.3660
Randolph 151 142588 637 8752 123509 9690 0.4 6.1 86.6 6.8 0.5026
Richmond 153 45710 933 14473 28756 1548 2.0 31.7 62.9 3.4 0.8498
Robeson 155 134576 52120 32599 39500 10357 38.7 24.2 29.4 7.7 1.2680
Rockingham 157 91898 477 17041 69614 4766 0.5 18.5 75.8 5.2 0.7036
Rowan 159 138694 312 22329 108360 7693 0.2 16.1 78.1 5.5 0.6610
Rutherford 161 66701 325 6893 56997 2486 0.5 10.3 85.5 3.7 0.5175
Sampson 163 63713 1219 16240 39660 6594 1.9 25.5 62.2 10.3 0.9539
Scotland 165 35711 3777 13730 16249 1955 10.6 38.4 45.5 5.5 1.1224
Stanly 167 60610 208 6369 51212 2821 0.3 10.5 84.5 4.7 0.5414
Stokes 169 46453 271 1932 43386 864 0.6 4.2 93.4 1.9 0.3002
Surry 171 72767 276 2689 66972 2830 0.4 3.7 92.0 3.9 0.3457
Swain 173 14234 3952 186 9143 953 27.8 1.3 64.2 6.7 0.8778
Transylvania 175 33062 117 1273 29879 1793 0.4 3.9 90.4 5.4 0.3949
Tyrrell 177 4128 85 1512 2302 229 2.1 36.6 55.8 5.5 0.9339
Union 179 217614 724 25260 177613 14017 0.3 11.6 81.6 6.4 0.6114
Vance 181 44508 752 22162 19355 2239 1.7 49.8 43.5 5.0 0.9287
Wake 183 998576 3405 205682 669687 119802 0.3 20.6 67.1 12.0 0.8671
Warren 185 20324 980 10328 8046 970 4.8 50.8 39.6 4.8 1.0022
Washington 187 12503 18 6079 5815 591 0.1 48.6 46.5 4.7 0.8603
Watauga 189 52745 170 632 49587 2356 0.3 1.2 94.0 4.5 0.2684
Wayne 191 124447 289 38504 74099 11555 0.2 30.9 59.5 9.3 0.9064
Wilkes 193 68888 133 2945 62792 3018 0.2 4.3 91.2 4.4 0.3683
Wilson 195 81617 515 31846 41325 7931 0.6 39.0 50.6 9.7 0.9703
Yadkin 197 37819 111 1285 34612 1811 0.3 3.4 91.5 4.8 0.3586
Yancey 199 17599 76 206 16991 326 0.4 1.2 96.5 1.9 0.1834